ENGS/PHYS 100:  Schedule



pdf version

 

 
ENGS/PHYS 100. Methods in Applied Mathematics I

 

 

Class Time

MWF 11:15 am - 12:20 pm, Tue 12-12:50 pm (X-hour)

Classroom

MacLean 132 (Engineering Sciences Center)

Instructor

William Lotko

Grade Basis

Weekly homework (50%); Midterm Exam (25%); Final Exam (25%)

 

 

Week 1

Function of a Complex Variable

Wednesday

Sep 23

Algebra, complex plane, Argand diagram, de Moivre’s theorem, trigonometric series

3

 

 

Friday

Sep 25

Analytic functions, Cauchy-Riemann conditions, Riemann sheets, branch cuts

24.1 - 24.6

 

 

 

 

Week 2

Function of a Complex Variable

Monday

Sep 28

Contour integrals, Cauchy’s Theorem and integral formula, Taylor expansion

24.8 - 24.11

 

 

Wednesday

Sep 30

Analytic continuation, Laurent series, poles, calculus of residues

24.12

 

 

Friday

Oct 2

Contour integration: Examples

24.13

 

 

 

Week 3

Finite Dimensional Vector Spaces

Monday

Oct 5

Contour integration with branch cuts

24.13

 

Tuesday

Oct 6

X-Hr 12-12:50p

Linear vector spaces, algebra, linear independence, basis set, transpose, inner product

8.1

 

 

Wednesday

Oct 7

Matrix operations, linear operators, classes of operators, examples

8.2-8.12

 

 

Friday

Oct 9

Eigenvectors/values, inequalities, Gram-Schmidt orthogonalization

8.13

 

 

 

Week 4

Finite Dimensional Vector Spaces

Monday

Oct 12

Unitary operators, eigenvalues/vectors, diagonalization, characteristic equation

8.13 - 8.14

 

 

Wednesday

Oct 14

Change of basis, orthogonal transformation, eigenproblems

8.15 - 8.17

 

 

Friday

Oct 16

Systems of linear differential equations

8.18, 9.1

 

 

 

 

Week 5

Linear Differential Equations

Monday

Oct 19

Second order DEs, ordinary and singular points, series solution

16.1

 

 

Wednesday

Oct 21

Series solution and Method of Frobenius

16.2

 

 

Friday

Oct 23

Series expansion around a singular point, Bessel’s equation and functions

16.3

 

 

 

 

Week 6

Linear Differential Equations

Monday

Oct 26

Missing solutions, logarithmic solution

16.4

 

 

Wednesday

Oct 28

Legendre's equation and polynomial solutions

16.6

 

 

Friday

Oct 30

Nonhomogenous problem, families of ODES

Notes

 

 

 

 

Week 7

Infinite Dimensional Vector Space

Monday

Nov 2

Hilbert space, self-adjoint operator, complete and orthonormal sets

17.1 - 17.2

 

 

Wednesday

Nov 4

Eigenfunction expansions

 

Friday

Nov 6

Boundary value problems, Sturm-Liouville problem

17.4

 

 

 

 

Week 8

Infinite Dimensional Vector Spaces

Monday

Nov 9

Green's functions

17.5 - 17.6

 

 

Wednesday

Nov 11

Gamma function

18, Notes

 

 

Friday

Nov 13

Hypergeometric and special functions

18, Notes

 

 

 

 

Week 9

Integral Transforms

Monday

Nov 16

Orthogonal polynomials

18, Notes

 

 

Wednesday

Nov 18

Fourier transform, convolution, Parseval relation, uncertainty principle

13.1

 

 

Friday

Nov 20

Laplace transform, an application leading to Abel’s integral equation

13.2

 

 

 

 

Week 10/11

Integral Transforms

Monday

Nov 23

General approach to the derivation of transform pairs

Notes

 

 

Monday

Nov 30

Other transform pairs

Notes

 

 

Wednesday

Dec 2

Applications